# Principal currents for a pair of unitary operators

### About this Title

**Joel Pincus** and **Shao Jie Zhou**

Publication: Memoirs of the American Mathematical Society

Publication Year
1994: Volume 109, Number 522

ISBNs: 978-0-8218-2609-6 (print); 978-1-4704-0099-6 (online)

DOI: http://dx.doi.org/10.1090/memo/0522

MathSciNet review: 1243584

MSC: Primary 47-02; Secondary 30E25, 47A45, 47B20

### Table of Contents

**Chapters**

- 0. Introduction
- 1. The geometry associated with eigenvalues
- 2. The dilation space solution of the symbol Riemann Hilbert problem
- 3. The principal current for the operator-tuple $\{P_1, P_2, W_1, W_2\}$
- 4. Estimates
- 5. The criterion for eigenvalues
- 6. The $N(\omega )$ operator
- 7. The characteristic operator function of $T_1$
- 8. Localization and the “cut-down” property
- 9. The joint essential spectrum
- 10. Singular integral representations
- 11. Toeplitz operators with unimodular symbols
- 12. $C_{11}$-contraction operators with (1,1) deficiency indices